Impact and interest

Abstract

Let LN+1 be a linear differential operator of order N + 1 with constant coefficients
and real eigenvalues λ 1, ..., λ N+1, let E( N+1) be the space of all C∞-solutions of
LN+1 on the real line.We show that for N 2 and n = 2, ...,N, there is a recurrence
relation from suitable subspaces εn to εn+1 involving real-analytic functions, and
with εN+1 = E(Λ N+1) if and only if contiguous eigenvalues are equally spaced.

Publisher's statement:This is the author.s version of a work that was accepted for publication in Journal of Approximation Theory. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in J. M. Aldaz, O. Kounchev, H. Render : On real-analytic recurrence relations for cardinal exponential B-splines. Journal of Approximation Theory, 145 2007-10, pp.253-265. DOI:10.1016/j.jat.2006.09.004

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